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The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, textit{the leader}, that is responsible for a null controllability property; additionally, we have a control textit{the follower} that solves a robust control objective. That means, that we seek for a saddle point of a cost functional. In this way, the follower control is not sensitive to a broad class of external disturbances. As far as we know, the idea of combining robustness with a Stackelberg strategy is new in literature
This paper concerns a controllability problem for blowup points on heat equation. It can be described as follows: In the absence of control, the solution to the linear heat system globally exists in a bounded domain $Omega$. While, for a given time $
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic equation with first order terms.
In a separable Hilbert space $X$, we study the linear evolution equation begin{equation*} u(t)+Au(t)+p(t)Bu(t)=0, end{equation*} where $A$ is an accretive self-adjoint linear operator, $B$ is a bounded linear operator on $X$, and $pin L^2_{loc}(0,+in
In this paper we study the internal exact controllability for a second order linear evolution equation defined in a two-component domain. On the interface we prescribe a jump of the solution proportional to the conormal derivatives, meanwhile a homog
We address the following problem: given a Riemannian manifold $(M,g)$ and small parameters $varepsilon>0$ and $v>0$, is it possible to find $T>0$ and an absolutely continuous map $x:[0,T]rightarrow M, tmapsto x(t)$ satisfying $|dot{x}|_{infty}leq v$